The aim is to carefully introduce the basic ideas and concepts and transverse and longitudinal beam dynamics, for students working in all areas of accelerator physics.
Pre-requisites
Electromagnetism, mechanics, relativity at undergraduate level.
Syllabus
Introduction
Let’s look at a synchrotron
Periodicity and stability
Hierarchy of beam descriptions
SHM and the pendulum
Newton and Hamilton
Hill’s equations
Beams and magnets
Derivation of Hill’s equations
The transfer matrix approach
Matrix properness
Lattice functions
Lattice functions
The Courant-Synder formalism
How to transform the lattice functions
Stability
Tune
Optics and lattice design
The FODO cell
Lattice design
Mini beta insertions
Principles of lattice design
Optical structures
Errors in our lattice
Field errors
Closed orbit distortion
Tune shifts
Real particles
Dispersion
Momentum compaction Chromaticity
Emittance
Longitudinal dynamics
The principle of phase stability
The pill-box cavity and real cavities
Longitudinal dynamics
Buckets and bunches
Aim
The aim is to carefully introduce the basic ideas and concepts and transverse and longitudinal beam dynamics, for students working in all areas of accelerator physics.Pre-requisites
Electromagnetism, mechanics, relativity at undergraduate level.Syllabus
Let’s look at a synchrotron
Periodicity and stability
Hierarchy of beam descriptions
SHM and the pendulum
Newton and Hamilton
Beams and magnets
Derivation of Hill’s equations
The transfer matrix approach
Matrix properness
Lattice functions
The Courant-Synder formalism
How to transform the lattice functions
Stability
Tune
The FODO cell
Lattice design
Mini beta insertions
Principles of lattice design
Optical structures
Field errors
Closed orbit distortion
Tune shifts
Dispersion
Momentum compaction Chromaticity
Emittance
The principle of phase stability
The pill-box cavity and real cavities
Longitudinal dynamics
Buckets and bunches
Synchrotron radiation
Damping effects (directed reading)
Lecture Notes
Part 1, Part 2